Downing Street communications chief Andy Coulson has quit after admitting the News of the World phone-hacking row was making his job impossible.

In a personal statement issued by Number 10, Mr Coulson said the drip-drip of claims about illegal eavesdropping under his editorship meant he could not "give the 110% needed".

"I stand by what I’ve said about those events but when the spokesman needs a spokesman it’s time to move on," he added.

The Prime Minister said he was "very sorry" that Mr Coulson felt "compelled" to go after months of intense pressure, and thanked him for his "complete professionalism" over the past three and a half years.

But critics insisted the resignation was "long overdue", and questioned Mr Cameron’s judgment in recruiting the former journalist in the first place.

The timing also sparked accusations that the Government was trying to "bury bad news" while Tony Blair was appearing at the Iraq Inquiry, and with the furore over shadow chancellor Alan Johnson’s departure still raging.

Last week Mr Cameron refused to confirm or deny reports that his communications director had offered to resign to spare the coalition further damage.

But he conceded that Mr Coulson was "extremely embarrassed" about claims that he knew famous people’s phone voicemails were being accessed.

Just an hour before the resignation today, Mr Cameron was asked during a visit to RAF Brize Norton whether he still had faith in Mr Coulson.

"You know what I have said about this in the past," he replied. "I have got nothing to add to that and I think he’s done a very good job for the Government."

It is believed Mr Coulson informed Mr Cameron of his intention to leave on Wednesday. No decision has yet been taken on a replacement.

Mr Coulson resigned as editor of the News of the World in 2007 after the paper’s former royal editor Clive Goodman and private investigator Glenn Mulcaire were jailed for phone hacking.

Although he accepted ultimate responsibility for the illegal activities, he has always denied knowing they were taking place. A Scotland Yard investigation resulted in no further charges.

But a number of public figures are still taking civil legal action against the newspaper, and documents disclosed in those cases have sparked fresh developments.

It emerged earlier this month that News of the World executive Ian Edmondson has been suspended as a result of claims in a case brought by actress Sienna Miller.

Police subsequently wrote to the newspaper asking for any new evidence staff had on the case.

The Crown Prosecution Service (CPS) has tasked a senior QC to "comprehensively" re-examine material amassed as part of the original inquiry and any new evidence.

In his resignation statement today, Mr Coulson said: "Nothing is more important than the Government’s task of getting this country back on its feet.

"Unfortunately continued coverage of events connected to my old job at the News of the World has made it difficult for me to give the 110% needed in this role.

"I stand by what I’ve said about those events but when the spokesman needs a spokesman it’s time to move on.

"I’ll leave within the next few weeks and will do so wishing the Prime Minister, his family and his brilliant and dedicated team the very best for what I’m sure will be a long and successful future in Government."

Mr Cameron replied: "I am very sorry that Andy Coulson has decided to resign as my director of communications, although I understand that the continuing pressures on him and his family mean that he feels compelled to do so.

"Andy has told me that the focus on him was impeding his ability to do his job and was starting to prove a distraction for the Government.

"During his time working for me, Andy has carried out his role with complete professionalism. He has been a brilliant member of my team and has thrown himself at the job with skill and dedication. He can be extremely proud of the role he has played, including for the last eight months in Government."

Labour leader Ed Miliband said there had been "real questions" about Mr Coulson’s ability to do his job with the "cloud" of allegations hanging over him.

"He’s now done the right thing," Mr Miliband told reporters on a visit to Scotland. "I think there are questions about David Cameron’s judgment about hanging on to him as long as he did."

Labour frontbencher Chris Bryant said he hoped the police would now conduct a thorough investigation into the phone hacking.

"To say this is long overdue is an understatement," he added. "Andy Coulson should never have been appointed in the first place."

A Downing Street source branded the idea that it had been trying to "bury bad news" as "complete rubbish".

"We have knocked two very bad news stories of Labour’s off the top of the bulletins," they said.

The Prime Minister was informed on Wednesday evening, and the permanent secretary at Number 10, Jeremy Heywood, was told yesterday.

The source also insisted the resignation had not been prompted by any particular development in the phone hacking saga.